Now, he has a chance to fulfill that dream after the Indians selected him in the fifth round (No. 173 overall) of the First-Year Player Draft on Tuesday.
"Everyone loves each other there and vibes off each other to make everything better," Baker said of Western. "[Pitching coach] Jeremy Beard worked with me literally every single day. I was throwing like 88-90 [mph] in fall ball, and then after Christmas break, I was throwing 95. It showed what can happen when coaches really care about you."
It wasn't long after that when scouts began coming in droves to watch Baker pitch. He had developed a nasty slider and a reliable curveball to complement his mid-90s fastball, and he was dominating opposing hitters. Baker went 13-0 with a 1.91 ERA in 16 starts this spring, helping Western advance to the Junior College World Series.
At first, Baker was surprised by the attention. He wasn't used to it.
"I got there for fall ball and one scout wanted to talk to me," he said. "I was like, 'Wow.' I was pretty excited about that. Then after Christmas break, when I was throwing even harder, more and more scouts wanted to talk to me.
"Right then and there, I knew I could definitely compete with everyone else."
Baker, 20, should help strengthen the Indians' farm system pitching, which took a hit when right-hander Austin Adams had shoulder surgery in May. That's especially true considering many experts rated Baker as one of the top 50 players available and expected him to be gone by the second round.
"I heard I was supposed to go earlier," Baker said, "but I'm still happy with where I went. A lot of teams called my advisor and they were saying they were going to pick me up in the second round. That didn't happen. I was a little upset, but I still got picked pretty high, so I can't really be upset about that."
Baker envisions himself as a starter in the future, but he's OK with whatever the Indians organization has in mind for him.
"I don't really care how I get there," he said, "as long as I get there."
Baker isn't there yet, but he's closer than he ever thought he'd be. He went from being a JUCO walk-on to a high Draft pick in only one year.
Because he's from Alaska, Baker knows the odds are stacked against him to play for the Indians.
But the way he sees it, the odds have been stacked against him all along.
"I've come so far," Baker said. "I was pretty much a nobody last year. This year, I really bumped it up and showed people that I'm here. It just makes me so happy and proud."